LMFDB - Embedded newform 864.2.y.a.97.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(97,864)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("864.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.y (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			97.8
Character	$\chi$	$=$	864.97
Dual form			864.2.y.a.481.8

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.72103 + 0.195105i) q^{3} +(0.517524 + 0.188363i) q^{5} +(-0.780902 + 4.42872i) q^{7} +(2.92387 + 0.671562i) q^{9} +O(q^{10})$	\(q+(1.72103 + 0.195105i) q^{3} +(0.517524 + 0.188363i) q^{5} +(-0.780902 + 4.42872i) q^{7} +(2.92387 + 0.671562i) q^{9} +(-1.48871 + 0.541847i) q^{11} +(-1.64780 + 1.38267i) q^{13} +(0.853922 + 0.425150i) q^{15} +(1.17725 + 2.03906i) q^{17} +(0.0655666 - 0.113565i) q^{19} +(-2.20802 + 7.46958i) q^{21} +(-0.0132392 - 0.0750834i) q^{23} +(-3.59787 - 3.01897i) q^{25} +(4.90103 + 1.72624i) q^{27} +(-4.07315 - 3.41778i) q^{29} +(1.30041 + 7.37501i) q^{31} +(-2.66783 + 0.642078i) q^{33} +(-1.23834 + 2.14487i) q^{35} +(1.49305 + 2.58604i) q^{37} +(-3.10567 + 2.05811i) q^{39} +(8.65824 - 7.26512i) q^{41} +(-0.587142 + 0.213702i) q^{43} +(1.38667 + 0.898299i) q^{45} +(-0.384448 + 2.18031i) q^{47} +(-12.4259 - 4.52265i) q^{49} +(1.62825 + 3.73896i) q^{51} +9.94034 q^{53} -0.872508 q^{55} +(0.134999 - 0.182656i) q^{57} +(5.48455 + 1.99621i) q^{59} +(2.08556 - 11.8278i) q^{61} +(-5.25741 + 12.4246i) q^{63} +(-1.11322 + 0.405179i) q^{65} +(10.0979 - 8.47314i) q^{67} +(-0.00813594 - 0.131804i) q^{69} +(6.94216 + 12.0242i) q^{71} +(1.48961 - 2.58009i) q^{73} +(-5.60302 - 5.89770i) q^{75} +(-1.23715 - 7.01621i) q^{77} +(1.90882 + 1.60169i) q^{79} +(8.09801 + 3.92712i) q^{81} +(-3.50308 - 2.93943i) q^{83} +(0.225172 + 1.27701i) q^{85} +(-6.34317 - 6.67678i) q^{87} +(-0.417704 + 0.723484i) q^{89} +(-4.83667 - 8.37736i) q^{91} +(0.799146 + 12.9463i) q^{93} +(0.0553237 - 0.0464221i) q^{95} +(-12.6541 + 4.60571i) q^{97} +(-4.71668 + 0.584527i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 12 q^{9}+O(q^{10}) $ 48 * q - 12 * q^9	$ 48 q - 12 q^{9} - 12 q^{17} - 48 q^{21} + 24 q^{25} + 6 q^{29} - 6 q^{33} + 30 q^{37} - 12 q^{41} + 30 q^{45} - 6 q^{49} - 36 q^{53} - 6 q^{57} - 12 q^{61} - 60 q^{65} - 78 q^{69} + 48 q^{73} - 12 q^{77} - 36 q^{81} + 102 q^{85} - 66 q^{89} + 36 q^{93} + 6 q^{97}+O(q^{100}) $ 48 * q - 12 * q^9 - 12 * q^17 - 48 * q^21 + 24 * q^25 + 6 * q^29 - 6 * q^33 + 30 * q^37 - 12 * q^41 + 30 * q^45 - 6 * q^49 - 36 * q^53 - 6 * q^57 - 12 * q^61 - 60 * q^65 - 78 * q^69 + 48 * q^73 - 12 * q^77 - 36 * q^81 + 102 * q^85 - 66 * q^89 + 36 * q^93 + 6 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$1$	$e\left(\frac{2}{9}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	1.72103	+	0.195105i	0.993635	+	0.112644i
$3$	1.72103	+	0.195105i	0.993635	+	0.112644i
$4$		0			0
$5$	0.517524	+	0.188363i	0.231444	+	0.0842386i	0.455139	−	0.890421i	$-0.349590\pi$
$5$	0.517524	+	0.188363i	0.231444	+	0.0842386i	−0.223695	+	0.974659i	$0.571812\pi$
$6$		0			0
$7$	−0.780902	+	4.42872i	−0.295153	+	1.67390i	0.371426	+	0.928463i	$0.378869\pi$
$7$	−0.780902	+	4.42872i	−0.295153	+	1.67390i	−0.666579	+	0.745434i	$0.732242\pi$
$8$		0			0
$9$	2.92387	+	0.671562i	0.974623	+	0.223854i
$10$		0			0
$11$	−1.48871	+	0.541847i	−0.448863	+	0.163373i	−0.556554	−	0.830812i	$-0.687877\pi$
$11$	−1.48871	+	0.541847i	−0.448863	+	0.163373i	0.107690	+	0.994184i	$0.465654\pi$
$12$		0			0
$13$	−1.64780	+	1.38267i	−0.457017	+	0.383483i	−0.842032	−	0.539427i	$-0.818641\pi$
$13$	−1.64780	+	1.38267i	−0.457017	+	0.383483i	0.385015	+	0.922910i	$0.374196\pi$
$14$		0			0
$15$	0.853922	+	0.425150i	0.220482	+	0.109773i
$16$		0			0
$17$	1.17725	+	2.03906i	0.285525	+	0.494544i	0.972736	−	0.231914i	$-0.0744987\pi$
$17$	1.17725	+	2.03906i	0.285525	+	0.494544i	−0.687211	+	0.726458i	$0.741165\pi$
$18$		0			0
$19$	0.0655666	−	0.113565i	0.0150420	−	0.0260535i	−0.858406	−	0.512970i	$-0.828545\pi$
$19$	0.0655666	−	0.113565i	0.0150420	−	0.0260535i	0.873448	+	0.486917i	$0.161878\pi$
$20$		0			0
$21$	−2.20802	+	7.46958i	−0.481829	+	1.63000i
$22$		0			0
$23$	−0.0132392	−	0.0750834i	−0.00276057	−	0.0156560i	0.983396	−	0.181471i	$-0.0580857\pi$
$23$	−0.0132392	−	0.0750834i	−0.00276057	−	0.0156560i	−0.986157	+	0.165815i	$0.946975\pi$
$24$		0			0
$25$	−3.59787	−	3.01897i	−0.719574	−	0.603795i
$26$		0			0
$27$	4.90103	+	1.72624i	0.943204	+	0.332214i
$28$		0			0
$29$	−4.07315	−	3.41778i	−0.756364	−	0.634665i	0.180813	−	0.983517i	$-0.442127\pi$
$29$	−4.07315	−	3.41778i	−0.756364	−	0.634665i	−0.937178	+	0.348852i	$0.886571\pi$
$30$		0			0
$31$	1.30041	+	7.37501i	0.233561	+	1.32459i	0.845623	+	0.533781i	$0.179229\pi$
$31$	1.30041	+	7.37501i	0.233561	+	1.32459i	−0.612062	+	0.790810i	$0.709660\pi$
$32$		0			0
$33$	−2.66783	+	0.642078i	−0.464409	+	0.111771i
$34$		0			0
$35$	−1.23834	+	2.14487i	−0.209318	+	0.362550i
$36$		0			0
$37$	1.49305	+	2.58604i	0.245456	+	0.425142i	0.962260	−	0.272133i	$-0.0877290\pi$
$37$	1.49305	+	2.58604i	0.245456	+	0.425142i	−0.716804	+	0.697275i	$0.754396\pi$
$38$		0			0
$39$	−3.10567	+	2.05811i	−0.497305	+	0.329562i
$40$		0			0
$41$	8.65824	−	7.26512i	1.35219	−	1.13462i	0.373879	−	0.927477i	$-0.378027\pi$
$41$	8.65824	−	7.26512i	1.35219	−	1.13462i	0.978310	−	0.207144i	$-0.0664170\pi$
$42$		0			0
$43$	−0.587142	+	0.213702i	−0.0895384	+	0.0325893i	−0.386401	−	0.922331i	$-0.626282\pi$
$43$	−0.587142	+	0.213702i	−0.0895384	+	0.0325893i	0.296863	+	0.954920i	$0.404060\pi$
$44$		0			0
$45$	1.38667	+	0.898299i	0.206713	+	0.133910i
$46$		0			0
$47$	−0.384448	+	2.18031i	−0.0560775	+	0.318031i	−0.999924	−	0.0123540i	$-0.996067\pi$
$47$	−0.384448	+	2.18031i	−0.0560775	+	0.318031i	0.943846	+	0.330385i	$0.107179\pi$
$48$		0			0
$49$	−12.4259	−	4.52265i	−1.77512	−	0.646092i
$50$		0			0
$51$	1.62825	+	3.73896i	0.228001	+	0.523559i
$52$		0			0
$53$	9.94034			1.36541			0.682706	−	0.730694i	$-0.260803\pi$
$53$	9.94034			1.36541			0.682706	+	0.730694i	$0.260803\pi$
$54$		0			0
$55$	−0.872508			−0.117649
$56$		0			0
$57$	0.134999	−	0.182656i	0.0178810	−	0.0241933i
$58$		0			0
$59$	5.48455	+	1.99621i	0.714028	+	0.259885i	0.673388	−	0.739289i	$-0.264838\pi$
$59$	5.48455	+	1.99621i	0.714028	+	0.259885i	0.0406394	+	0.999174i	$0.487061\pi$
$60$		0			0
$61$	2.08556	−	11.8278i	0.267029	−	1.51439i	−0.496167	−	0.868227i	$-0.665260\pi$
$61$	2.08556	−	11.8278i	0.267029	−	1.51439i	0.763196	−	0.646167i	$-0.223629\pi$
$62$		0			0
$63$	−5.25741	+	12.4246i	−0.662371	+	1.56535i
$64$		0			0
$65$	−1.11322	+	0.405179i	−0.138078	+	0.0502562i
$66$		0			0
$67$	10.0979	−	8.47314i	1.23365	−	1.03516i	0.235661	−	0.971835i	$-0.424274\pi$
$67$	10.0979	−	8.47314i	1.23365	−	1.03516i	0.997993	−	0.0633237i	$-0.0201700\pi$
$68$		0			0
$69$	−0.00813594	−	0.131804i	−0.000979452	−	0.0158673i
$70$		0			0
$71$	6.94216	+	12.0242i	0.823883	+	1.42701i	0.902770	+	0.430123i	$0.141530\pi$
$71$	6.94216	+	12.0242i	0.823883	+	1.42701i	−0.0788875	+	0.996884i	$0.525137\pi$
$72$		0			0
$73$	1.48961	−	2.58009i	0.174346	−	0.301976i	−0.765589	−	0.643330i	$-0.777552\pi$
$73$	1.48961	−	2.58009i	0.174346	−	0.301976i	0.939935	+	0.341354i	$0.110886\pi$
$74$		0			0
$75$	−5.60302	−	5.89770i	−0.646981	−	0.681007i
$76$		0			0
$77$	−1.23715	−	7.01621i	−0.140986	−	0.799571i
$78$		0			0
$79$	1.90882	+	1.60169i	0.214758	+	0.180204i	0.743821	−	0.668379i	$-0.233012\pi$
$79$	1.90882	+	1.60169i	0.214758	+	0.180204i	−0.529062	+	0.848583i	$0.677456\pi$
$80$		0			0
$81$	8.09801	+	3.92712i	0.899779	+	0.436346i
$82$		0			0
$83$	−3.50308	−	2.93943i	−0.384513	−	0.322644i	0.429958	−	0.902849i	$-0.358528\pi$
$83$	−3.50308	−	2.93943i	−0.384513	−	0.322644i	−0.814471	+	0.580204i	$0.802973\pi$
$84$		0			0
$85$	0.225172	+	1.27701i	0.0244233	+	0.138511i
$86$		0			0
$87$	−6.34317	−	6.67678i	−0.680059	−	0.715826i
$88$		0			0
$89$	−0.417704	+	0.723484i	−0.0442765	+	0.0766892i	−0.887314	−	0.461165i	$-0.847432\pi$
$89$	−0.417704	+	0.723484i	−0.0442765	+	0.0766892i	0.843038	+	0.537854i	$0.180765\pi$
$90$		0			0
$91$	−4.83667	−	8.37736i	−0.507021	−	0.878186i
$92$		0			0
$93$	0.799146	+	12.9463i	0.0828676	+	1.34247i
$94$		0			0
$95$	0.0553237	−	0.0464221i	0.00567609	−	0.00476281i
$96$		0			0
$97$	−12.6541	+	4.60571i	−1.28483	+	0.467639i	−0.892026	−	0.451985i	$-0.850716\pi$
$97$	−12.6541	+	4.60571i	−1.28483	+	0.467639i	−0.392801	+	0.919623i	$0.628494\pi$
$98$		0			0
$99$	−4.71668	+	0.584527i	−0.474044	+	0.0587471i
$100$		0			0
$101$	2.34476	−	13.2978i	0.233312	−	1.32318i	−0.612826	−	0.790218i	$-0.709967\pi$
$101$	2.34476	−	13.2978i	0.233312	−	1.32318i	0.846139	−	0.532963i	$-0.178921\pi$
$102$		0			0
$103$	−8.26000	−	3.00640i	−0.813882	−	0.296229i	−0.0986558	−	0.995122i	$-0.531454\pi$
$103$	−8.26000	−	3.00640i	−0.813882	−	0.296229i	−0.715227	+	0.698893i	$0.753677\pi$
$104$		0			0
$105$	−2.54970	+	3.44978i	−0.248825	+	0.336664i
$106$		0			0
$107$	13.1333			1.26964			0.634820	−	0.772660i	$-0.281074\pi$
$107$	13.1333			1.26964			0.634820	+	0.772660i	$0.281074\pi$
$108$		0			0
$109$	−13.9405			−1.33525			−0.667627	−	0.744496i	$-0.732690\pi$
$109$	−13.9405			−1.33525			−0.667627	+	0.744496i	$0.732690\pi$
$110$		0			0
$111$	2.06503	+	4.74194i	0.196004	+	0.450085i
$112$		0			0
$113$	8.99749	+	3.27482i	0.846413	+	0.308069i	0.728577	−	0.684964i	$-0.240182\pi$
$113$	8.99749	+	3.27482i	0.846413	+	0.308069i	0.117836	+	0.993033i	$0.462404\pi$
$114$		0			0
$115$	0.00729134	−	0.0413513i	0.000679921	−	0.00385602i
$116$		0			0
$117$	−5.74649	+	2.93614i	−0.531263	+	0.271446i
$118$		0			0
$119$	−9.94972	+	3.62140i	−0.912090	+	0.331973i
$120$		0			0
$121$	−6.50383	+	5.45736i	−0.591257	+	0.496123i
$122$		0			0
$123$	16.3185	−	10.8142i	1.47139	−	0.975085i
$124$		0			0
$125$	−2.67016	−	4.62486i	−0.238827	−	0.413660i
$126$		0			0
$127$	6.78563	−	11.7531i	0.602128	−	1.04292i	−0.390371	−	0.920658i	$-0.627653\pi$
$127$	6.78563	−	11.7531i	0.602128	−	1.04292i	0.992498	−	0.122258i	$-0.0390135\pi$
$128$		0			0
$129$	−1.05218	+	0.253233i	−0.0926395	+	0.0222959i
$130$		0			0
$131$	−2.93176	−	16.6268i	−0.256149	−	1.45269i	−0.793105	−	0.609084i	$-0.791537\pi$
$131$	−2.93176	−	16.6268i	−0.256149	−	1.45269i	0.536956	−	0.843610i	$-0.319574\pi$
$132$		0			0
$133$	0.451745	+	0.379059i	0.0391712	+	0.0328686i
$134$		0			0
$135$	2.21124	+	1.81654i	0.190313	+	0.156343i
$136$		0			0
$137$	17.0281	+	14.2883i	1.45481	+	1.22073i	0.928975	+	0.370143i	$0.120691\pi$
$137$	17.0281	+	14.2883i	1.45481	+	1.22073i	0.525834	+	0.850587i	$0.323753\pi$
$138$		0			0
$139$	3.46833	+	19.6699i	0.294180	+	1.66838i	0.670518	+	0.741893i	$0.266072\pi$
$139$	3.46833	+	19.6699i	0.294180	+	1.66838i	−0.376338	+	0.926482i	$0.622817\pi$
$140$		0			0
$141$	−1.08703	+	3.67737i	−0.0915448	+	0.309690i
$142$		0			0
$143$	1.70390	−	2.95125i	0.142487	−	0.246796i
$144$		0			0
$145$	−1.46417	−	2.53601i	−0.121592	−	0.210604i
$146$		0			0
$147$	−20.5029	−	10.2079i	−1.69105	−	0.841937i
$148$		0			0
$149$	−1.16549	+	0.977961i	−0.0954805	+	0.0801177i	−0.689278	−	0.724497i	$-0.742072\pi$
$149$	−1.16549	+	0.977961i	−0.0954805	+	0.0801177i	0.593798	+	0.804614i	$0.297628\pi$
$150$		0			0
$151$	−16.1135	+	5.86482i	−1.31130	+	0.477273i	−0.900659	−	0.434527i	$-0.856916\pi$
$151$	−16.1135	+	5.86482i	−1.31130	+	0.477273i	−0.410637	+	0.911799i	$0.634694\pi$
$152$		0			0
$153$	2.07277	+	6.75253i	0.167574	+	0.545910i
$154$		0			0
$155$	−0.716186	+	4.06169i	−0.0575255	+	0.326243i
$156$		0			0
$157$	9.42937	+	3.43201i	0.752546	+	0.273904i	0.689677	−	0.724118i	$-0.257753\pi$
$157$	9.42937	+	3.43201i	0.752546	+	0.273904i	0.0628690	+	0.998022i	$0.479975\pi$
$158$		0			0
$159$	17.1076	+	1.93941i	1.35672	+	0.153805i
$160$		0			0
$161$	0.342862			0.0270213
$162$		0			0
$163$	−7.72273			−0.604891			−0.302445	−	0.953167i	$-0.597803\pi$
$163$	−7.72273			−0.604891			−0.302445	+	0.953167i	$0.597803\pi$
$164$		0			0
$165$	−1.50161	−	0.170231i	−0.116900	−	0.0132524i
$166$		0			0
$167$	−10.5315	−	3.83314i	−0.814949	−	0.296617i	−0.0992826	−	0.995059i	$-0.531655\pi$
$167$	−10.5315	−	3.83314i	−0.814949	−	0.296617i	−0.715667	+	0.698442i	$0.753877\pi$
$168$		0			0
$169$	−1.45395	+	8.24579i	−0.111843	+	0.634291i
$170$		0			0
$171$	0.267974	−	0.288016i	0.0204925	−	0.0220252i
$172$		0			0
$173$	11.3605	−	4.13489i	0.863724	−	0.314370i	0.128101	−	0.991761i	$-0.459112\pi$
$173$	11.3605	−	4.13489i	0.863724	−	0.314370i	0.735623	+	0.677391i	$0.236890\pi$
$174$		0			0
$175$	16.1798	−	13.5764i	1.22307	−	1.02628i
$176$		0			0
$177$	9.04959	+	4.50560i	0.680209	+	0.338662i
$178$		0			0
$179$	−7.69847	−	13.3341i	−0.575410	−	0.996640i	−0.995997	−	0.0893876i	$-0.971509\pi$
$179$	−7.69847	−	13.3341i	−0.575410	−	0.996640i	0.420586	−	0.907252i	$-0.361824\pi$
$180$		0			0
$181$	4.88887	−	8.46776i	0.363387	−	0.629404i	−0.625129	−	0.780521i	$-0.714954\pi$
$181$	4.88887	−	8.46776i	0.363387	−	0.629404i	0.988516	+	0.151117i	$0.0482871\pi$
$182$		0			0
$183$	5.89697	−	19.9491i	0.435916	−	1.47468i
$184$		0			0
$185$	0.285574	+	1.61957i	0.0209958	+	0.119073i
$186$		0			0
$187$	−2.85744	−	2.39768i	−0.208957	−	0.175336i
$188$		0			0
$189$	−11.4722	+	20.3573i	−0.834482	+	1.48077i
$190$		0			0
$191$	−12.8728	−	10.8015i	−0.931440	−	0.781571i	0.0446355	−	0.999003i	$-0.485787\pi$
$191$	−12.8728	−	10.8015i	−0.931440	−	0.781571i	−0.976075	+	0.217432i	$0.930232\pi$
$192$		0			0
$193$	−3.05688	−	17.3364i	−0.220039	−	1.24790i	−0.871945	−	0.489604i	$-0.837141\pi$
$193$	−3.05688	−	17.3364i	−0.220039	−	1.24790i	0.651906	−	0.758300i	$-0.273970\pi$
$194$		0			0
$195$	−1.99493	+	0.480129i	−0.142860	+	0.0343827i
$196$		0			0
$197$	10.3743	−	17.9687i	0.739135	−	1.28022i	−0.213750	−	0.976888i	$-0.568568\pi$
$197$	10.3743	−	17.9687i	0.739135	−	1.28022i	0.952885	−	0.303331i	$-0.0980988\pi$
$198$		0			0
$199$	−7.55892	−	13.0924i	−0.535837	−	0.928097i	−0.999122	−	0.0418881i	$-0.986663\pi$
$199$	−7.55892	−	13.0924i	−0.535837	−	0.928097i	0.463285	−	0.886209i	$-0.346671\pi$
$200$		0			0
$201$	19.0319	−	12.6124i	1.34241	−	0.889607i
$202$		0			0
$203$	18.3171	−	15.3699i	1.28561	−	1.07875i
$204$		0			0
$205$	5.84933	−	2.12898i	0.408535	−	0.148695i
$206$		0			0
$207$	0.0117134	−	0.228425i	0.000814135	−	0.0158766i
$208$		0			0
$209$	−0.0360751	+	0.204592i	−0.00249537	+	0.0141519i
$210$		0			0
$211$	6.15653	+	2.24079i	0.423833	+	0.154263i	0.545126	−	0.838354i	$-0.316482\pi$
$211$	6.15653	+	2.24079i	0.423833	+	0.154263i	−0.121293	+	0.992617i	$0.538704\pi$
$212$		0			0
$213$	9.60167	+	22.0484i	0.657895	+	1.51073i
$214$		0			0
$215$	−0.344114			−0.0234684
$216$		0			0
$217$	−33.6773			−2.28617
$218$		0			0
$219$	3.06705	−	4.14977i	0.207252	−	0.280415i
$220$		0			0
$221$	−4.75921	−	1.73221i	−0.320139	−	0.116521i
$222$		0			0
$223$	−2.84871	+	16.1558i	−0.190764	+	1.08187i	0.727560	+	0.686044i	$0.240654\pi$
$223$	−2.84871	+	16.1558i	−0.190764	+	1.08187i	−0.918324	+	0.395831i	$0.870457\pi$
$224$		0			0
$225$	−8.49228	−	11.2433i	−0.566152	−	0.749551i
$226$		0			0
$227$	−18.7531	+	6.82558i	−1.24469	+	0.453030i	−0.878604	−	0.477551i	$-0.841524\pi$
$227$	−18.7531	+	6.82558i	−1.24469	+	0.453030i	−0.366086	+	0.930581i	$0.619302\pi$
$228$		0			0
$229$	8.94667	−	7.50715i	0.591213	−	0.496086i	−0.297395	−	0.954755i	$-0.596118\pi$
$229$	8.94667	−	7.50715i	0.591213	−	0.496086i	0.888608	+	0.458668i	$0.151673\pi$
$230$		0			0
$231$	−0.760267	−	12.3165i	−0.0500219	−	0.810363i
$232$		0			0
$233$	−0.828869	−	1.43564i	−0.0543010	−	0.0940521i	0.837597	−	0.546288i	$-0.183960\pi$
$233$	−0.828869	−	1.43564i	−0.0543010	−	0.0940521i	−0.891898	+	0.452236i	$0.850626\pi$
$234$		0			0
$235$	−0.609651	+	1.05595i	−0.0397693	+	0.0688824i
$236$		0			0
$237$	2.97263	+	3.12896i	0.193093	+	0.203248i
$238$		0			0
$239$	−4.35272	−	24.6855i	−0.281554	−	1.59677i	−0.717340	−	0.696723i	$-0.754641\pi$
$239$	−4.35272	−	24.6855i	−0.281554	−	1.59677i	0.435786	−	0.900050i	$-0.356470\pi$
$240$		0			0
$241$	−5.15079	−	4.32203i	−0.331792	−	0.278406i	0.461638	−	0.887069i	$-0.347262\pi$
$241$	−5.15079	−	4.32203i	−0.331792	−	0.278406i	−0.793429	+	0.608662i	$0.791706\pi$
$242$		0			0
$243$	13.1707	+	8.33863i	0.844900	+	0.534924i
$244$		0			0
$245$	−5.57878	−	4.68115i	−0.356415	−	0.299068i
$246$		0			0
$247$	0.0489816	+	0.277789i	0.00311663	+	0.0176753i
$248$		0			0
$249$	−5.45539	−	5.74231i	−0.345721	−	0.363904i
$250$		0			0
$251$	−8.47513	+	14.6794i	−0.534945	+	0.926553i	0.464221	+	0.885720i	$0.346334\pi$
$251$	−8.47513	+	14.6794i	−0.534945	+	0.926553i	−0.999166	+	0.0408330i	$0.986999\pi$
$252$		0			0
$253$	0.0603931	+	0.104604i	0.00379688	+	0.00657639i
$254$		0			0
$255$	0.138375	+	2.24170i	0.00866539	+	0.140381i
$256$		0			0
$257$	−13.8383	+	11.6117i	−0.863212	+	0.724320i	−0.962657	−	0.270723i	$-0.912737\pi$
$257$	−13.8383	+	11.6117i	−0.863212	+	0.724320i	0.0994459	+	0.995043i	$0.468293\pi$
$258$		0			0
$259$	−12.6187	+	4.59285i	−0.784091	+	0.285386i
$260$		0			0
$261$	−9.61410	−	12.7285i	−0.595098	−	0.787874i
$262$		0			0
$263$	2.32530	−	13.1874i	0.143384	−	0.813171i	−0.825267	−	0.564743i	$-0.808975\pi$
$263$	2.32530	−	13.1874i	0.143384	−	0.813171i	0.968651	−	0.248427i	$-0.0799137\pi$
$264$		0			0
$265$	5.14437	+	1.87240i	0.316016	+	0.115020i
$266$		0			0
$267$	−0.860035	+	1.16364i	−0.0526333	+	0.0712136i
$268$		0			0
$269$	−20.5015			−1.25000			−0.625000	−	0.780624i	$-0.714901\pi$
$269$	−20.5015			−1.25000			−0.625000	+	0.780624i	$0.714901\pi$
$270$		0			0
$271$	3.27670			0.199045			0.0995226	−	0.995035i	$-0.468268\pi$
$271$	3.27670			0.199045			0.0995226	+	0.995035i	$0.468268\pi$
$272$		0			0
$273$	−6.68958	−	15.3613i	−0.404872	−	0.929709i
$274$		0			0
$275$	6.99201	+	2.54488i	0.421634	+	0.153462i
$276$		0			0
$277$	−4.13219	+	23.4348i	−0.248279	+	1.40806i	0.564473	+	0.825451i	$0.309079\pi$
$277$	−4.13219	+	23.4348i	−0.248279	+	1.40806i	−0.812752	+	0.582609i	$0.802032\pi$
$278$		0			0
$279$	−1.15054	+	22.4369i	−0.0688808	+	1.34326i
$280$		0			0
$281$	8.72143	−	3.17434i	0.520277	−	0.189365i	−0.0685149	−	0.997650i	$-0.521826\pi$
$281$	8.72143	−	3.17434i	0.520277	−	0.189365i	0.588792	+	0.808285i	$0.299604\pi$
$282$		0			0
$283$	16.8464	−	14.1358i	1.00141	−	0.840284i	0.0142324	−	0.999899i	$-0.495470\pi$
$283$	16.8464	−	14.1358i	1.00141	−	0.840284i	0.987179	+	0.159614i	$0.0510251\pi$
$284$		0			0
$285$	0.104271	−	0.0690998i	0.00617647	−	0.00409312i
$286$		0			0
$287$	25.4139	+	44.0182i	1.50014	+	2.59831i
$288$		0			0
$289$	5.72816	−	9.92147i	0.336951	−	0.583616i
$290$		0			0
$291$	−22.6766	+	5.45767i	−1.32933	+	0.319935i
$292$		0			0
$293$	0.234577	+	1.33035i	0.0137042	+	0.0777201i	0.990893	−	0.134653i	$-0.0429919\pi$
$293$	0.234577	+	1.33035i	0.0137042	+	0.0777201i	−0.977189	+	0.212373i	$0.931881\pi$
$294$		0			0
$295$	2.46237	+	2.06618i	0.143365	+	0.120297i
$296$		0			0
$297$	−8.23158	+	0.0857392i	−0.477644	+	0.00497509i
$298$		0			0
$299$	0.125631	+	0.105417i	0.00726543	+	0.00609642i
$300$		0			0
$301$	−0.487926	−	2.76717i	−0.0281236	−	0.159497i
$302$		0			0
$303$	6.62986	−	22.4284i	0.380876	−	1.28848i
$304$		0			0
$305$	3.30725	−	5.72833i	0.189373	−	0.328003i
$306$		0			0
$307$	−8.82453	−	15.2845i	−0.503643	−	0.872335i	−0.999991	−	0.00421139i	$-0.998659\pi$
$307$	−8.82453	−	15.2845i	−0.503643	−	0.872335i	0.496348	−	0.868123i	$-0.334674\pi$
$308$		0			0
$309$	−13.6291	−	6.78566i	−0.775334	−	0.386022i
$310$		0			0
$311$	7.15667	−	6.00516i	0.405818	−	0.340521i	−0.416920	−	0.908943i	$-0.636890\pi$
$311$	7.15667	−	6.00516i	0.405818	−	0.340521i	0.822737	+	0.568422i	$0.192446\pi$
$312$		0			0
$313$	5.05181	−	1.83871i	0.285545	−	0.103930i	−0.195277	−	0.980748i	$-0.562561\pi$
$313$	5.05181	−	1.83871i	0.285545	−	0.103930i	0.480822	+	0.876818i	$0.340338\pi$
$314$		0			0
$315$	−5.06117	+	5.43970i	−0.285164	+	0.306493i
$316$		0			0
$317$	−2.36432	+	13.4087i	−0.132793	+	0.753109i	0.843578	+	0.537007i	$0.180445\pi$
$317$	−2.36432	+	13.4087i	−0.132793	+	0.753109i	−0.976371	+	0.216101i	$0.930666\pi$
$318$		0			0
$319$	7.91565	+	2.88106i	0.443191	+	0.161308i
$320$		0			0
$321$	22.6027	+	2.56236i	1.26156	+	0.143017i
$322$		0			0
$323$	0.308753			0.0171795
$324$		0			0
$325$	10.1028			0.560403
$326$		0			0
$327$	−23.9919	−	2.71985i	−1.32676	−	0.150408i
$328$		0			0
$329$	−9.35576	−	3.40522i	−0.515800	−	0.187736i
$330$		0			0
$331$	−1.00997	+	5.72783i	−0.0555130	+	0.314830i	−0.999902	−	0.0140005i	$-0.995543\pi$
$331$	−1.00997	+	5.72783i	−0.0555130	+	0.314830i	0.944389	+	0.328830i	$0.106654\pi$
$332$		0			0
$333$	2.62880	+	8.56391i	0.144057	+	0.469299i
$334$		0			0
$335$	6.82193	−	2.48298i	0.372722	−	0.135660i
$336$		0			0
$337$	9.06418	−	7.60575i	0.493757	−	0.414312i	−0.361613	−	0.932328i	$-0.617774\pi$
$337$	9.06418	−	7.60575i	0.493757	−	0.414312i	0.855371	+	0.518017i	$0.173329\pi$
$338$		0			0
$339$	14.8460	+	7.39151i	0.806323	+	0.401451i
$340$		0			0
$341$	−5.93206	−	10.2746i	−0.321239	−	0.556403i
$342$		0			0
$343$	13.9933	−	24.2371i	0.755566	−	1.30868i
$344$		0			0
$345$	0.0206164	−	0.0697441i	0.00110995	−	0.00375489i
$346$		0			0
$347$	3.41697	+	19.3786i	0.183432	+	1.04030i	0.927953	+	0.372697i	$0.121567\pi$
$347$	3.41697	+	19.3786i	0.183432	+	1.04030i	−0.744521	+	0.667599i	$0.767322\pi$
$348$		0			0
$349$	8.85788	+	7.43264i	0.474151	+	0.397860i	0.848306	−	0.529506i	$-0.177623\pi$
$349$	8.85788	+	7.43264i	0.474151	+	0.397860i	−0.374155	+	0.927366i	$0.622067\pi$
$350$		0			0
$351$	−10.4627	+	3.93200i	−0.558459	+	0.209875i
$352$		0			0
$353$	0.410646	+	0.344573i	0.0218565	+	0.0183398i	0.653650	−	0.756797i	$-0.273237\pi$
$353$	0.410646	+	0.344573i	0.0218565	+	0.0183398i	−0.631794	+	0.775136i	$0.717681\pi$
$354$		0			0
$355$	1.32782	+	7.53045i	0.0704734	+	0.399675i
$356$		0			0
$357$	−17.8303	+	4.29129i	−0.943679	+	0.227119i
$358$		0			0
$359$	5.00032	−	8.66081i	0.263907	−	0.457100i	−0.703370	−	0.710824i	$-0.748322\pi$
$359$	5.00032	−	8.66081i	0.263907	−	0.457100i	0.967277	+	0.253724i	$0.0816555\pi$
$360$		0			0
$361$	9.49140	+	16.4396i	0.499547	+	0.865242i
$362$		0			0
$363$	−12.2580	+	8.12333i	−0.643379	+	0.426364i
$364$		0			0
$365$	1.25690	−	1.05467i	0.0657894	−	0.0552038i
$366$		0			0
$367$	−5.98683	+	2.17903i	−0.312510	+	0.113744i	−0.493513	−	0.869738i	$-0.664288\pi$
$367$	−5.98683	+	2.17903i	−0.312510	+	0.113744i	0.181004	+	0.983482i	$0.442065\pi$
$368$		0			0
$369$	30.1945	−	15.4277i	1.57186	−	0.803135i
$370$		0			0
$371$	−7.76243	+	44.0230i	−0.403006	+	2.28556i
$372$		0			0
$373$	1.46046	+	0.531564i	0.0756198	+	0.0275233i	0.379553	−	0.925170i	$-0.376078\pi$
$373$	1.46046	+	0.531564i	0.0756198	+	0.0275233i	−0.303933	+	0.952693i	$0.598300\pi$
$374$		0			0
$375$	−3.69309	−	8.48047i	−0.190710	−	0.437930i
$376$		0			0
$377$	11.4374			0.589055
$378$		0			0
$379$	−23.2556			−1.19456			−0.597280	−	0.802033i	$-0.703752\pi$
$379$	−23.2556			−1.19456			−0.597280	+	0.802033i	$0.703752\pi$
$380$		0			0
$381$	13.9713	−	18.9034i	0.715773	−	0.968452i
$382$		0			0
$383$	7.20985	+	2.62417i	0.368406	+	0.134089i	0.519588	−	0.854417i	$-0.326086\pi$
$383$	7.20985	+	2.62417i	0.368406	+	0.134089i	−0.151182	+	0.988506i	$0.548308\pi$
$384$		0			0
$385$	0.681343	−	3.86409i	0.0347245	−	0.196932i
$386$		0			0
$387$	−1.86024	+	0.230535i	−0.0945614	+	0.0117188i
$388$		0			0
$389$	−6.27429	+	2.28365i	−0.318119	+	0.115786i	−0.496144	−	0.868240i	$-0.665251\pi$
$389$	−6.27429	+	2.28365i	−0.318119	+	0.115786i	0.178025	+	0.984026i	$0.443029\pi$
$390$		0			0
$391$	0.137514	−	0.115388i	0.00695436	−	0.00583540i
$392$		0			0
$393$	−1.80166	−	29.1873i	−0.0908818	−	1.47230i
$394$		0			0
$395$	0.686159	+	1.18846i	0.0345244	+	0.0597980i
$396$		0			0
$397$	12.5136	−	21.6742i	0.628039	−	1.08780i	−0.359906	−	0.932989i	$-0.617191\pi$
$397$	12.5136	−	21.6742i	0.628039	−	1.08780i	0.987945	−	0.154807i	$-0.0494755\pi$
$398$		0			0
$399$	0.703509	+	0.740508i	0.0352195	+	0.0370718i
$400$		0			0
$401$	6.10210	+	34.6068i	0.304725	+	1.72818i	0.624798	+	0.780786i	$0.285181\pi$
$401$	6.10210	+	34.6068i	0.304725	+	1.72818i	−0.320074	+	0.947393i	$0.603708\pi$
$402$		0			0
$403$	−12.3400	−	10.3545i	−0.614699	−	0.515794i
$404$		0			0
$405$	3.45119	+	3.55774i	0.171491	+	0.176786i
$406$		0			0
$407$	−3.62395	−	3.04086i	−0.179633	−	0.150730i
$408$		0			0
$409$	5.87277	+	33.3061i	0.290390	+	1.64688i	0.685372	+	0.728193i	$0.259640\pi$
$409$	5.87277	+	33.3061i	0.290390	+	1.64688i	−0.394982	+	0.918689i	$0.629249\pi$
$410$		0			0
$411$	26.5181	+	27.9128i	1.30804	+	1.37684i
$412$		0			0
$413$	−13.1236	+	22.7307i	−0.645768	+	1.11850i
$414$		0			0
$415$	−1.25925	−	2.18108i	−0.0618139	−	0.107065i
$416$		0			0
$417$	2.13140	+	34.5290i	0.104375	+	1.69089i
$418$		0			0
$419$	20.9444	−	17.5744i	1.02320	−	0.858567i	0.0331743	−	0.999450i	$-0.489438\pi$
$419$	20.9444	−	17.5744i	1.02320	−	0.858567i	0.990026	+	0.140882i	$0.0449939\pi$
$420$		0			0
$421$	−2.93343	+	1.06768i	−0.142967	+	0.0520357i	−0.412513	−	0.910952i	$-0.635349\pi$
$421$	−2.93343	+	1.06768i	−0.142967	+	0.0520357i	0.269546	+	0.962988i	$0.413126\pi$
$422$		0			0
$423$	−2.58829	+	6.11676i	−0.125847	+	0.297407i
$424$		0			0
$425$	1.92026	−	10.8904i	0.0931465	−	0.528260i
$426$		0			0
$427$	50.7533	+	18.4727i	2.45613	+	0.893957i
$428$		0			0
$429$	3.50826	−	4.74673i	0.169381	−	0.229174i
$430$		0			0
$431$	22.5026			1.08391			0.541955	−	0.840407i	$-0.317684\pi$
$431$	22.5026			1.08391			0.541955	+	0.840407i	$0.317684\pi$
$432$		0			0
$433$	−12.8313			−0.616631			−0.308316	−	0.951284i	$-0.599765\pi$
$433$	−12.8313			−0.616631			−0.308316	+	0.951284i	$0.599765\pi$
$434$		0			0
$435$	−2.02508	−	4.65021i	−0.0970953	−	0.222961i
$436$		0			0
$437$	−0.00939488	−	0.00341946i	−0.000449418	−	0.000163575i
$438$		0			0
$439$	−6.59930	+	37.4265i	−0.314967	+	1.78627i	0.257436	+	0.966295i	$0.417122\pi$
$439$	−6.59930	+	37.4265i	−0.314967	+	1.78627i	−0.572403	+	0.819972i	$0.693989\pi$
$440$		0			0
$441$	−33.2944	−	21.5684i	−1.58545	−	1.02706i
$442$		0			0
$443$	−35.0789	+	12.7677i	−1.66665	+	0.606610i	−0.991386	−	0.130969i	$-0.958191\pi$
$443$	−35.0789	+	12.7677i	−1.66665	+	0.606610i	−0.675261	+	0.737579i	$0.735969\pi$
$444$		0			0
$445$	−0.352450	+	0.295740i	−0.0167077	+	0.0140194i
$446$		0			0
$447$	−2.19664	+	1.45570i	−0.103898	+	0.0688525i
$448$		0			0
$449$	11.5191	+	19.9516i	0.543618	+	0.941574i	0.998693	+	0.0511203i	$0.0162792\pi$
$449$	11.5191	+	19.9516i	0.543618	+	0.941574i	−0.455075	+	0.890453i	$0.650387\pi$
$450$		0			0
$451$	−8.95303	+	15.5071i	−0.421582	+	0.730201i
$452$		0			0
$453$	−28.8760	+	6.94970i	−1.35671	+	0.326526i
$454$		0			0
$455$	−0.925106	−	5.24653i	−0.0433696	−	0.245961i
$456$		0			0
$457$	3.64232	+	3.05627i	0.170381	+	0.142966i	0.723991	−	0.689810i	$-0.242306\pi$
$457$	3.64232	+	3.05627i	0.170381	+	0.142966i	−0.553610	+	0.832776i	$0.686750\pi$
$458$		0			0
$459$	2.24985	+	12.0257i	0.105014	+	0.561311i
$460$		0			0
$461$	−4.60357	−	3.86286i	−0.214410	−	0.179911i	0.529257	−	0.848461i	$-0.322471\pi$
$461$	−4.60357	−	3.86286i	−0.214410	−	0.179911i	−0.743667	+	0.668550i	$0.766915\pi$
$462$		0			0
$463$	−0.806835	−	4.57579i	−0.0374968	−	0.212655i	0.960303	−	0.278961i	$-0.0899899\pi$
$463$	−0.806835	−	4.57579i	−0.0374968	−	0.212655i	−0.997799	+	0.0663056i	$0.978879\pi$
$464$		0			0
$465$	−2.02503	+	6.85056i	−0.0939086	+	0.317687i
$466$		0			0
$467$	−15.0136	+	26.0044i	−0.694749	+	1.20334i	0.275517	+	0.961296i	$0.411151\pi$
$467$	−15.0136	+	26.0044i	−0.694749	+	1.20334i	−0.970265	+	0.242044i	$0.922182\pi$
$468$		0			0
$469$	29.6397	+	51.3374i	1.36863	+	2.37054i
$470$		0			0
$471$	15.5586	+	7.74630i	0.716902	+	0.356931i
$472$		0			0
$473$	0.758291	−	0.636282i	0.0348663	−	0.0292563i
$474$		0			0
$475$	−0.578749	+	0.210647i	−0.0265548	+	0.00966517i
$476$		0			0
$477$	29.0643	+	6.67555i	1.33076	+	0.305653i
$478$		0			0
$479$	2.18414	−	12.3869i	0.0997959	−	0.565971i	−0.893376	−	0.449310i	$-0.851670\pi$
$479$	2.18414	−	12.3869i	0.0997959	−	0.565971i	0.993172	−	0.116661i	$-0.0372190\pi$
$480$		0			0
$481$	−6.03587	−	2.19688i	−0.275212	−	0.100169i
$482$		0			0
$483$	0.590074	+	0.0668940i	0.0268493	+	0.00304378i
$484$		0			0
$485$	−7.41633			−0.336758
$486$		0			0
$487$	17.3705			0.787132			0.393566	−	0.919296i	$-0.371241\pi$
$487$	17.3705			0.787132			0.393566	+	0.919296i	$0.371241\pi$
$488$		0			0
$489$	−13.2910	−	1.50674i	−0.601041	−	0.0681372i
$490$		0			0
$491$	−9.66489	−	3.51773i	−0.436170	−	0.158753i	0.114597	−	0.993412i	$-0.463442\pi$
$491$	−9.66489	−	3.51773i	−0.436170	−	0.158753i	−0.550767	+	0.834659i	$0.685665\pi$
$492$		0			0
$493$	2.17393	−	12.3290i	0.0979088	−	0.555268i
$494$		0			0
$495$	−2.55110	−	0.585943i	−0.114663	−	0.0263362i
$496$		0			0
$497$	−58.6728	+	21.3551i	−2.63183	+	0.957909i
$498$		0			0
$499$	−17.3754	+	14.5797i	−0.777830	+	0.652677i	−0.942701	−	0.333638i	$-0.891724\pi$
$499$	−17.3754	+	14.5797i	−0.777830	+	0.652677i	0.164871	+	0.986315i	$0.447279\pi$
$500$		0			0
$501$	−17.3771	−	8.65168i	−0.776350	−	0.386528i
$502$		0			0
$503$	5.26001	+	9.11060i	0.234532	+	0.406222i	0.959137	−	0.282943i	$-0.0913108\pi$
$503$	5.26001	+	9.11060i	0.234532	+	0.406222i	−0.724604	+	0.689165i	$0.757977\pi$
$504$		0			0
$505$	3.71829	−	6.44026i	0.165462	−	0.286588i
$506$		0			0
$507$	−4.11109	+	13.9075i	−0.182580	+	0.617656i
$508$		0			0
$509$	−4.43561	−	25.1556i	−0.196605	−	1.11500i	−0.910115	−	0.414357i	$-0.864007\pi$
$509$	−4.43561	−	25.1556i	−0.196605	−	1.11500i	0.713510	−	0.700645i	$-0.247105\pi$
$510$		0			0
$511$	10.2632	+	8.61187i	0.454018	+	0.380967i
$512$		0			0
$513$	0.517384	−	0.443401i	0.0228430	−	0.0195766i
$514$		0			0
$515$	−3.70846	−	3.11176i	−0.163414	−	0.137121i
$516$		0			0
$517$	−0.609062	−	3.45416i	−0.0267865	−	0.151914i
$518$		0			0
$519$	20.3585	−	4.89976i	0.893638	−	0.215076i
$520$		0			0
$521$	−12.8378	+	22.2358i	−0.562436	+	0.974168i	0.434847	+	0.900504i	$0.356802\pi$
$521$	−12.8378	+	22.2358i	−0.562436	+	0.974168i	−0.997283	+	0.0736635i	$0.976531\pi$
$522$		0			0
$523$	1.12294	+	1.94499i	0.0491027	+	0.0850483i	0.889532	−	0.456873i	$-0.151031\pi$
$523$	1.12294	+	1.94499i	0.0491027	+	0.0850483i	−0.840429	+	0.541921i	$0.817697\pi$
$524$		0			0
$525$	30.4946	−	20.2087i	1.33089	−	0.881978i
$526$		0			0
$527$	−13.5072	+	11.3339i	−0.588381	+	0.493710i
$528$		0			0
$529$	21.6075	−	7.86448i	0.939455	−	0.341934i
$530$		0			0
$531$	14.6955	+	9.51988i	0.637731	+	0.413127i
$532$		0			0
$533$	−4.22178	+	23.9429i	−0.182866	+	1.03708i
$534$		0			0
$535$	6.79678	+	2.47383i	0.293850	+	0.106953i
$536$		0			0
$537$	−10.6477	−	24.4504i	−0.459483	−	1.05511i
$538$		0			0
$539$	20.9491			0.902342
$540$		0			0
$541$	11.8211			0.508230			0.254115	−	0.967174i	$-0.418216\pi$
$541$	11.8211			0.508230			0.254115	+	0.967174i	$0.418216\pi$
$542$		0			0
$543$	10.0660	−	13.6194i	0.431972	−	0.584465i
$544$		0			0
$545$	−7.21452	−	2.62587i	−0.309036	−	0.112480i
$546$		0			0
$547$	−1.48947	+	8.44721i	−0.0636852	+	0.361177i	0.936266	+	0.351292i	$0.114258\pi$
$547$	−1.48947	+	8.44721i	−0.0636852	+	0.361177i	−0.999951	+	0.00988475i	$0.996854\pi$
$548$		0			0
$549$	14.0410	−	33.1823i	0.599255	−	1.41619i
$550$		0			0
$551$	−0.655201	+	0.238474i	−0.0279125	+	0.0101593i
$552$		0			0
$553$	−8.58401	+	7.20284i	−0.365029	+	0.306296i
$554$		0			0
$555$	0.175495	+	2.84304i	0.00744933	+	0.120681i
$556$		0			0
$557$	8.53150	+	14.7770i	0.361491	+	0.626121i	0.988207	−	0.153127i	$-0.0489344\pi$
$557$	8.53150	+	14.7770i	0.361491	+	0.626121i	−0.626715	+	0.779248i	$0.715601\pi$
$558$		0			0
$559$	0.672013	−	1.16396i	0.0284231	−	0.0492303i
$560$		0			0
$561$	−4.44994	−	4.68397i	−0.187876	−	0.197757i
$562$		0			0
$563$	−6.26297	−	35.5191i	−0.263953	−	1.49695i	−0.772001	−	0.635621i	$-0.780744\pi$
$563$	−6.26297	−	35.5191i	−0.263953	−	1.49695i	0.508048	−	0.861329i	$-0.330367\pi$
$564$		0			0
$565$	4.03956	+	3.38959i	0.169946	+	0.142601i
$566$		0			0
$567$	−23.7158	+	32.7971i	−0.995971	+	1.37735i
$568$		0			0
$569$	−3.52807	−	2.96041i	−0.147905	−	0.124107i	0.565833	−	0.824520i	$-0.308555\pi$
$569$	−3.52807	−	2.96041i	−0.147905	−	0.124107i	−0.713738	+	0.700413i	$0.752999\pi$
$570$		0			0
$571$	1.75165	+	9.93411i	0.0733044	+	0.415730i	0.999273	+	0.0381288i	$0.0121397\pi$
$571$	1.75165	+	9.93411i	0.0733044	+	0.415730i	−0.925968	+	0.377601i	$0.876749\pi$
$572$		0			0
$573$	−20.0469	−	21.1013i	−0.837473	−	0.881517i
$574$		0			0
$575$	−0.179042	+	0.310109i	−0.00746656	+	0.0129325i
$576$		0			0
$577$	20.6464	+	35.7607i	0.859522	+	1.48874i	0.872386	+	0.488818i	$0.162572\pi$
$577$	20.6464	+	35.7607i	0.859522	+	1.48874i	−0.0128636	+	0.999917i	$0.504095\pi$
$578$		0			0
$579$	−1.87855	−	30.4329i	−0.0780700	−	1.26475i
$580$		0			0
$581$	15.7535	−	13.2187i	0.653564	−	0.548405i
$582$		0			0
$583$	−14.7983	+	5.38614i	−0.612883	+	0.223071i
$584$		0			0
$585$	−3.52701	+	0.437094i	−0.145824	+	0.0180716i
$586$		0			0
$587$	1.41340	−	8.01580i	0.0583373	−	0.330848i	−0.941646	−	0.336605i	$-0.890721\pi$
$587$	1.41340	−	8.01580i	0.0583373	−	0.330848i	0.999983	+	0.00575708i	$0.00183255\pi$
$588$		0			0
$589$	0.922805	+	0.335873i	0.0380235	+	0.0138394i
$590$		0			0
$591$	21.3602	−	28.9006i	0.878640	−	1.18881i
$592$		0			0
$593$	3.78859			0.155579			0.0777893	−	0.996970i	$-0.475214\pi$
$593$	3.78859			0.155579			0.0777893	+	0.996970i	$0.475214\pi$
$594$		0			0
$595$	−5.83136			−0.239062
$596$		0			0
$597$	−10.4547	−	24.0072i	−0.427882	−	0.982549i
$598$		0			0
$599$	−41.9331	−	15.2624i	−1.71334	−	0.623604i	−0.716109	−	0.697988i	$-0.754079\pi$
$599$	−41.9331	−	15.2624i	−1.71334	−	0.623604i	−0.997230	+	0.0743840i	$0.976301\pi$
$600$		0			0
$601$	5.10224	−	28.9362i	0.208125	−	1.18033i	−0.684322	−	0.729180i	$-0.739902\pi$
$601$	5.10224	−	28.9362i	0.208125	−	1.18033i	0.892446	−	0.451153i	$-0.148987\pi$
$602$		0			0
$603$	35.2152	−	17.9930i	1.43407	−	0.732731i
$604$		0			0
$605$	−4.39385	+	1.59923i	−0.178635	+	0.0650180i
$606$		0			0
$607$	−23.3231	+	19.5704i	−0.946655	+	0.794338i	−0.978731	−	0.205147i	$-0.934233\pi$
$607$	−23.3231	+	19.5704i	−0.946655	+	0.794338i	0.0320758	+	0.999485i	$0.489788\pi$
$608$		0			0
$609$	34.5229	−	22.8782i	1.39894	−	0.927071i
$610$		0			0
$611$	−2.38115	−	4.12428i	−0.0963311	−	0.166850i
$612$		0			0
$613$	14.3169	−	24.7976i	0.578253	−	1.00156i	−0.417426	−	0.908711i	$-0.637068\pi$
$613$	14.3169	−	24.7976i	0.578253	−	1.00156i	0.995680	−	0.0928535i	$-0.0295988\pi$
$614$		0			0
$615$	10.4822	−	2.52280i	0.422684	−	0.101729i
$616$		0			0
$617$	−4.57548	−	25.9489i	−0.184202	−	1.04466i	−0.926976	−	0.375120i	$-0.877602\pi$
$617$	−4.57548	−	25.9489i	−0.184202	−	1.04466i	0.742774	−	0.669542i	$-0.233510\pi$
$618$		0			0
$619$	−0.272269	−	0.228461i	−0.0109434	−	0.00918262i	0.637300	−	0.770616i	$-0.280051\pi$
$619$	−0.272269	−	0.228461i	−0.0109434	−	0.00918262i	−0.648243	+	0.761434i	$0.724496\pi$
$620$		0			0
$621$	0.0647259	−	0.390840i	0.00259736	−	0.0156839i
$622$		0			0
$623$	−2.87792	−	2.41486i	−0.115301	−	0.0967494i
$624$		0			0
$625$	3.56714	+	20.2302i	0.142685	+	0.809209i
$626$		0			0
$627$	−0.102003	+	0.345070i	−0.00407361	+	0.0137808i
$628$		0			0
$629$	−3.51539	+	6.08883i	−0.140168	+	0.242777i
$630$		0			0
$631$	−5.07486	−	8.78991i	−0.202027	−	0.349921i	0.747155	−	0.664650i	$-0.231419\pi$
$631$	−5.07486	−	8.78991i	−0.202027	−	0.349921i	−0.949181	+	0.314730i	$0.898086\pi$
$632$		0			0
$633$	10.1584	+	5.05763i	0.403759	+	0.201023i
$634$		0			0
$635$	5.72557	−	4.80433i	0.227212	−	0.190654i
$636$		0			0
$637$	26.7286	−	9.72843i	1.05903	−	0.385454i
$638$		0			0
$639$	12.2230	+	39.8192i	0.483534	+	1.57522i
$640$		0			0
$641$	5.17069	−	29.3245i	0.204230	−	1.15825i	−0.694416	−	0.719573i	$-0.744337\pi$
$641$	5.17069	−	29.3245i	0.204230	−	1.15825i	0.898647	−	0.438673i	$-0.144551\pi$
$642$		0			0
$643$	21.7445	+	7.91435i	0.857519	+	0.312111i	0.733102	−	0.680119i	$-0.238072\pi$
$643$	21.7445	+	7.91435i	0.857519	+	0.312111i	0.124417	+	0.992230i	$0.460294\pi$
$644$		0			0
$645$	−0.592229	−	0.0671383i	−0.0233190	−	0.00264357i
$646$		0			0
$647$	−25.4188			−0.999315			−0.499658	−	0.866223i	$-0.666541\pi$
$647$	−25.4188			−0.999315			−0.499658	+	0.866223i	$0.666541\pi$
$648$		0			0
$649$	−9.24655			−0.362959
$650$		0			0
$651$	−57.9596	−	6.57061i	−2.27162	−	0.257523i
$652$		0			0
$653$	−0.824384	−	0.300051i	−0.0322606	−	0.0117419i	0.325839	−	0.945425i	$-0.394353\pi$
$653$	−0.824384	−	0.300051i	−0.0322606	−	0.0117419i	−0.358100	+	0.933683i	$0.616575\pi$
$654$		0			0
$655$	1.61463	−	9.15703i	0.0630889	−	0.357795i
$656$		0			0
$657$	6.08812	−	6.54346i	0.237520	−	0.255285i
$658$		0			0
$659$	1.12848	−	0.410732i	0.0439592	−	0.0159999i	−0.319947	−	0.947435i	$-0.603665\pi$
$659$	1.12848	−	0.410732i	0.0439592	−	0.0159999i	0.363906	+	0.931436i	$0.381443\pi$
$660$		0			0
$661$	−20.3165	+	17.0475i	−0.790219	+	0.663072i	−0.945800	−	0.324751i	$-0.894720\pi$
$661$	−20.3165	+	17.0475i	−0.790219	+	0.663072i	0.155581	+	0.987823i	$0.450275\pi$
$662$		0			0
$663$	−7.85276	−	3.90973i	−0.304976	−	0.151841i
$664$		0			0
$665$	0.162388	+	0.281264i	0.00629713	+	0.0109070i
$666$		0			0
$667$	−0.202693	+	0.351075i	−0.00784830	+	0.0135937i
$668$		0			0
$669$	−8.05479	+	27.2488i	−0.311416	+	1.05350i
$670$		0			0
$671$	3.30406	+	18.7382i	0.127552	+	0.723381i
$672$		0			0
$673$	−6.03892	−	5.06726i	−0.232783	−	0.195328i	0.518933	−	0.854815i	$-0.326329\pi$
$673$	−6.03892	−	5.06726i	−0.232783	−	0.195328i	−0.751716	+	0.659486i	$0.770774\pi$
$674$		0			0
$675$	−12.4218	−	21.0069i	−0.478116	−	0.808554i
$676$		0			0
$677$	−21.6768	−	18.1890i	−0.833106	−	0.699059i	0.122896	−	0.992420i	$-0.460782\pi$
$677$	−21.6768	−	18.1890i	−0.833106	−	0.699059i	−0.956002	+	0.293361i	$0.905226\pi$
$678$		0			0
$679$	−10.5158	−	59.6379i	−0.403558	−	2.28869i
$680$		0			0
$681$	−33.6064	+	8.08819i	−1.28780	+	0.309940i
$682$		0			0
$683$	20.3815	−	35.3019i	0.779878	−	1.35079i	−0.152134	−	0.988360i	$-0.548614\pi$
$683$	20.3815	−	35.3019i	0.779878	−	1.35079i	0.932012	−	0.362428i	$-0.118052\pi$
$684$		0			0
$685$	6.12106	+	10.6020i	0.233874	+	0.405081i
$686$		0			0
$687$	16.8621	−	11.1745i	0.643331	−	0.426332i
$688$		0			0
$689$	−16.3797	+	13.7442i	−0.624016	+	0.523612i
$690$		0			0
$691$	−10.4737	+	3.81210i	−0.398437	+	0.145019i	−0.533464	−	0.845823i	$-0.679110\pi$
$691$	−10.4737	+	3.81210i	−0.398437	+	0.145019i	0.135027	+	0.990842i	$0.456888\pi$
$692$		0			0
$693$	1.09456	−	21.3453i	0.0415790	−	0.810840i
$694$		0			0
$695$	−1.91014	+	10.8329i	−0.0724556	+	0.410916i
$696$		0			0
$697$	25.0069	+	9.10177i	0.947205	+	0.344754i
$698$		0			0
$699$	−1.14640	−	2.63250i	−0.0433610	−	0.0995701i
$700$		0			0
$701$	−29.5796			−1.11721			−0.558603	−	0.829435i	$-0.688663\pi$
$701$	−29.5796			−1.11721			−0.558603	+	0.829435i	$0.688663\pi$
$702$		0			0
$703$	0.391577			0.0147686
$704$		0			0
$705$	−1.25525	+	1.69837i	−0.0472753	+	0.0639642i
$706$		0			0
$707$	57.0611	+	20.7686i	2.14600	+	0.781082i
$708$		0			0
$709$	−4.51526	+	25.6073i	−0.169574	+	0.961702i	0.774648	+	0.632393i	$0.217927\pi$
$709$	−4.51526	+	25.6073i	−0.169574	+	0.961702i	−0.944222	+	0.329310i	$0.893184\pi$
$710$		0			0
$711$	4.50549	+	5.96501i	0.168969	+	0.223705i
$712$		0			0
$713$	0.536525	−	0.195279i	0.0200930	−	0.00731326i
$714$		0			0
$715$	1.43772	−	1.20639i	0.0537676	−	0.0451163i
$716$		0			0
$717$	−2.67489	−	43.3337i	−0.0998955	−	1.61833i
$718$		0			0
$719$	9.79281	+	16.9616i	0.365210	+	0.632563i	0.988810	−	0.149181i	$-0.0476638\pi$
$719$	9.79281	+	16.9616i	0.365210	+	0.632563i	−0.623600	+	0.781744i	$0.714330\pi$
$720$		0			0
$721$	19.7647	−	34.2335i	0.736077	−	1.27492i
$722$		0			0
$723$	−8.02141	−	8.44327i	−0.298319	−	0.314009i
$724$		0			0
$725$	4.33649	+	24.5934i	0.161053	+	0.913378i
$726$		0			0
$727$	15.4800	+	12.9892i	0.574120	+	0.481744i	0.883010	−	0.469354i	$-0.155513\pi$
$727$	15.4800	+	12.9892i	0.574120	+	0.481744i	−0.308890	+	0.951098i	$0.599958\pi$
$728$		0			0
$729$	21.0402	+	16.9207i	0.779267	+	0.626692i
$730$		0			0
$731$	−1.12696	−	0.945636i	−0.0416823	−	0.0349756i
$732$		0			0
$733$	−1.52512	−	8.64940i	−0.0563317	−	0.319473i	0.943601	−	0.331085i	$-0.107415\pi$
$733$	−1.52512	−	8.64940i	−0.0563317	−	0.319473i	−0.999933	+	0.0116123i	$0.996304\pi$
$734$		0			0
$735$	−8.68792	−	9.14484i	−0.320459	−	0.337313i
$736$		0			0
$737$	−10.4417	+	18.0856i	−0.384625	+	0.666191i
$738$		0			0
$739$	0.350274	+	0.606693i	0.0128850	+	0.0223176i	0.872396	−	0.488800i	$-0.162565\pi$
$739$	0.350274	+	0.606693i	0.0128850	+	0.0223176i	−0.859511	+	0.511117i	$0.829232\pi$
$740$		0			0
$741$	0.0301008	+	0.487638i	0.00110578	+	0.0179138i
$742$		0			0
$743$	27.9763	−	23.4749i	1.02635	−	0.861211i	0.0359390	−	0.999354i	$-0.488558\pi$
$743$	27.9763	−	23.4749i	1.02635	−	0.861211i	0.990412	+	0.138143i	$0.0441133\pi$
$744$		0			0
$745$	−0.787380	+	0.286583i	−0.0288474	+	0.0104996i
$746$		0			0
$747$	−8.26853	−	10.9470i	−0.302530	−	0.400531i
$748$		0			0
$749$	−10.2558	+	58.1635i	−0.374739	+	2.12525i
$750$		0			0
$751$	−1.69787	−	0.617975i	−0.0619562	−	0.0225502i	0.310856	−	0.950457i	$-0.399384\pi$
$751$	−1.69787	−	0.617975i	−0.0619562	−	0.0225502i	−0.372812	+	0.927907i	$0.621606\pi$
$752$		0			0
$753$	−17.4499	+	23.6100i	−0.635911	+	0.860397i
$754$		0			0
$755$	−9.44382			−0.343696
$756$		0			0
$757$	−42.5421			−1.54622			−0.773110	−	0.634272i	$-0.781300\pi$
$757$	−42.5421			−1.54622			−0.773110	+	0.634272i	$0.781300\pi$
$758$		0			0
$759$	0.0835294	+	0.191809i	0.00303193	+	0.00696223i
$760$		0			0
$761$	17.0121	+	6.19188i	0.616687	+	0.224456i	0.631427	−	0.775436i	$-0.282470\pi$
$761$	17.0121	+	6.19188i	0.616687	+	0.224456i	−0.0147397	+	0.999891i	$0.504692\pi$
$762$		0			0
$763$	10.8861	−	61.7383i	0.394104	−	2.23508i
$764$		0			0
$765$	−0.199220	+	3.88503i	−0.00720281	+	0.140464i
$766$		0			0
$767$	−11.7975	+	4.29395i	−0.425984	+	0.155046i
$768$		0			0
$769$	18.8463	−	15.8140i	0.679616	−	0.570266i	−0.236278	−	0.971686i	$-0.575928\pi$
$769$	18.8463	−	15.8140i	0.679616	−	0.570266i	0.915894	+	0.401420i	$0.131483\pi$
$770$		0			0
$771$	−26.0817	+	17.2842i	−0.939308	+	0.622475i
$772$		0			0
$773$	−0.910090	−	1.57632i	−0.0327337	−	0.0566964i	0.849194	−	0.528080i	$-0.177088\pi$
$773$	−0.910090	−	1.57632i	−0.0327337	−	0.0566964i	−0.881928	+	0.471384i	$0.843755\pi$
$774$		0			0
$775$	17.5862	−	30.4603i	0.631716	−	1.09416i
$776$		0			0
$777$	−22.6133	+	5.44244i	−0.811247	+	0.195246i
$778$		0			0
$779$	−0.257370	−	1.45962i	−0.00922125	−	0.0522963i
$780$		0			0
$781$	−16.8501	−	14.1389i	−0.602945	−	0.505931i
$782$		0			0
$783$	−14.0627	−	23.7818i	−0.502561	−	0.849894i
$784$		0			0
$785$	4.23346	+	3.55229i	0.151099	+	0.126787i
$786$		0			0
$787$	−6.75175	−	38.2911i	−0.240674	−	1.36493i	−0.830329	−	0.557274i	$-0.811847\pi$
$787$	−6.75175	−	38.2911i	−0.240674	−	1.36493i	0.589655	−	0.807655i	$-0.299264\pi$
$788$		0			0
$789$	6.57483	−	22.2422i	0.234070	−	0.791844i
$790$		0			0
$791$	−21.5294	+	37.2900i	−0.765497	+	1.32588i
$792$		0			0
$793$	12.9173	+	22.3735i	0.458708	+	0.794505i
$794$		0			0
$795$	8.48828	+	4.22614i	0.301048	+	0.149886i
$796$		0			0
$797$	−24.1371	+	20.2534i	−0.854979	+	0.717412i	−0.960880	−	0.276964i	$-0.910672\pi$
$797$	−24.1371	+	20.2534i	−0.854979	+	0.717412i	0.105902	+	0.994377i	$0.466227\pi$
$798$		0			0
$799$	−4.89837	+	1.78286i	−0.173292	+	0.0630731i
$800$		0			0
$801$	−1.70718	+	1.83486i	−0.0603201	+	0.0648316i
$802$		0			0
$803$	−0.819593	+	4.64814i	−0.0289228	+	0.164029i
$804$		0			0
$805$	0.177439	+	0.0645826i	0.00625391	+	0.00227624i
$806$		0			0
$807$	−35.2837	−	3.99995i	−1.24205	−	0.140805i
$808$		0			0
$809$	−7.67311			−0.269772			−0.134886	−	0.990861i	$-0.543067\pi$
$809$	−7.67311			−0.269772			−0.134886	+	0.990861i	$0.543067\pi$
$810$		0			0
$811$	−15.7110			−0.551687			−0.275844	−	0.961202i	$-0.588957\pi$
$811$	−15.7110			−0.551687			−0.275844	+	0.961202i	$0.588957\pi$
$812$		0			0
$813$	5.63929	+	0.639300i	0.197778	+	0.0224212i
$814$		0			0
$815$	−3.99670	−	1.45468i	−0.139998	−	0.0509552i
$816$		0			0
$817$	−0.0142279	+	0.0806904i	−0.000497771	+	0.00282300i
$818$		0			0
$819$	−8.51587	−	27.7424i	−0.297569	−	0.969398i
$820$		0			0
$821$	41.5358	−	15.1178i	1.44961	−	0.527614i	0.507126	−	0.861872i	$-0.330708\pi$
$821$	41.5358	−	15.1178i	1.44961	−	0.527614i	0.942482	+	0.334258i	$0.108486\pi$
$822$		0			0
$823$	−17.9960	+	15.1005i	−0.627302	+	0.526369i	−0.900089	−	0.435706i	$-0.856499\pi$
$823$	−17.9960	+	15.1005i	−0.627302	+	0.526369i	0.272787	+	0.962074i	$0.412054\pi$
$824$		0			0
$825$	11.5369	+	5.74399i	0.401664	+	0.199980i
$826$		0			0
$827$	−16.5226	−	28.6180i	−0.574548	−	0.995147i	−0.996091	−	0.0883382i	$-0.971844\pi$
$827$	−16.5226	−	28.6180i	−0.574548	−	0.995147i	0.421542	−	0.906809i	$-0.361489\pi$
$828$		0			0
$829$	5.53328	−	9.58392i	0.192179	−	0.332863i	−0.753793	−	0.657112i	$-0.771778\pi$
$829$	5.53328	−	9.58392i	0.192179	−	0.332863i	0.945972	+	0.324248i	$0.105111\pi$
$830$		0			0
$831$	−11.6839	+	39.5257i	−0.405308	+	1.37113i
$832$		0			0
$833$	−5.40642	−	30.6613i	−0.187321	−	1.06235i
$834$		0			0
$835$	−4.72826	−	3.96748i	−0.163628	−	0.137300i
$836$		0			0
$837$	−6.35765	+	38.3900i	−0.219752	+	1.32695i
$838$		0			0
$839$	−20.4800	−	17.1847i	−0.707047	−	0.593283i	0.216722	−	0.976233i	$-0.430464\pi$
$839$	−20.4800	−	17.1847i	−0.707047	−	0.593283i	−0.923769	+	0.382950i	$0.874908\pi$
$840$		0			0
$841$	−0.126464	−	0.717215i	−0.00436084	−	0.0247315i
$842$		0			0
$843$	15.6291	−	3.76153i	0.538296	−	0.129554i
$844$		0			0
$845$	−2.30566	+	3.99352i	−0.0793171	+	0.137381i
$846$		0			0
$847$	−19.0902	−	33.0653i	−0.655948	−	1.13614i
$848$		0			0
$849$	31.7510	−	21.0412i	1.08969	−	0.722133i
$850$		0			0
$851$	0.174402	−	0.146340i	0.00597841	−	0.00501648i
$852$		0			0
$853$	−18.7320	+	6.81788i	−0.641371	+	0.233440i	−0.642173	−	0.766560i	$-0.721967\pi$
$853$	−18.7320	+	6.81788i	−0.641371	+	0.233440i	0.000802052		1.00000i	$0.499745\pi$
$854$		0			0
$855$	0.192935	−	0.0985789i	0.00659822	−	0.00337133i
$856$		0			0
$857$	0.0823078	−	0.466791i	0.00281158	−	0.0159453i	−0.983370	−	0.181615i	$-0.941867\pi$
$857$	0.0823078	−	0.466791i	0.00281158	−	0.0159453i	0.986181	+	0.165670i	$0.0529786\pi$
$858$		0			0
$859$	23.3085	+	8.48361i	0.795276	+	0.289457i	0.707528	−	0.706686i	$-0.249811\pi$
$859$	23.3085	+	8.48361i	0.795276	+	0.289457i	0.0877487	+	0.996143i	$0.472033\pi$
$860$		0			0
$861$	35.1499	+	80.7149i	1.19791	+	2.75076i
$862$		0			0
$863$	48.6571			1.65631			0.828153	−	0.560502i	$-0.189392\pi$
$863$	48.6571			1.65631			0.828153	+	0.560502i	$0.189392\pi$
$864$		0			0
$865$	6.65820			0.226386
$866$		0			0
$867$	11.7941	−	15.9575i	0.400547	−	0.541946i
$868$		0			0
$869$	−3.70954	−	1.35016i	−0.125838	−	0.0458011i
$870$		0			0
$871$	−4.92376	+	27.9241i	−0.166835	+	0.946171i
$872$		0			0
$873$	−40.0919	+	4.96849i	−1.35690	+	0.168158i
$874$		0			0
$875$	22.5673	−	8.21384i	0.762915	−	0.277678i
$876$		0			0
$877$	6.64792	−	5.57826i	0.224484	−	0.188365i	−0.523608	−	0.851959i	$-0.675414\pi$
$877$	6.64792	−	5.57826i	0.224484	−	0.188365i	0.748092	+	0.663595i	$0.230970\pi$
$878$		0			0
$879$	0.144155	+	2.33534i	0.00486224	+	0.0787692i
$880$		0			0
$881$	−18.3761	−	31.8283i	−0.619106	−	1.07232i	−0.989649	−	0.143508i	$-0.954162\pi$
$881$	−18.3761	−	31.8283i	−0.619106	−	1.07232i	0.370543	−	0.928815i	$-0.379172\pi$
$882$		0			0
$883$	14.0318	−	24.3037i	0.472206	−	0.817885i	−0.527288	−	0.849687i	$-0.676791\pi$
$883$	14.0318	−	24.3037i	0.472206	−	0.817885i	0.999494	+	0.0318014i	$0.0101244\pi$
$884$		0			0
$885$	3.83469	+	4.03637i	0.128902	+	0.135681i
$886$		0			0
$887$	2.24672	+	12.7418i	0.0754375	+	0.427827i	0.999013	+	0.0444116i	$0.0141413\pi$
$887$	2.24672	+	12.7418i	0.0754375	+	0.427827i	−0.923576	+	0.383416i	$0.874748\pi$
$888$		0			0
$889$	46.7521	+	39.2296i	1.56801	+	1.31572i
$890$		0			0
$891$	−14.1835	−	1.45846i	−0.475165	−	0.0488603i
$892$		0			0
$893$	0.222399	+	0.186615i	0.00744231	+	0.00624484i
$894$		0			0
$895$	−1.47248	−	8.35084i	−0.0492195	−	0.279138i
$896$		0			0
$897$	0.195647	+	0.205937i	0.00653246	+	0.00687602i
$898$		0			0
$899$	19.9094	−	34.4840i	0.664014	−	1.15011i
$900$		0			0
$901$	11.7023	+	20.2689i	0.389859	+	0.675256i
$902$		0			0
$903$	−0.299846	−	4.85757i	−0.00997826	−	0.161650i
$904$		0			0
$905$	4.12512	−	3.46139i	0.137124	−	0.115060i
$906$		0			0
$907$	21.7467	−	7.91515i	0.722087	−	0.262818i	0.0452756	−	0.998975i	$-0.485583\pi$
$907$	21.7467	−	7.91515i	0.722087	−	0.262818i	0.676812	+	0.736156i	$0.263361\pi$
$908$		0			0
$909$	15.7861	−	37.3064i	0.523591	−	1.23737i
$910$		0			0
$911$	9.19459	−	52.1451i	0.304631	−	1.72765i	−0.320608	−	0.947212i	$-0.603887\pi$
$911$	9.19459	−	52.1451i	0.304631	−	1.72765i	0.625239	−	0.780434i	$-0.285002\pi$
$912$		0			0
$913$	6.80779	+	2.47783i	0.225305	+	0.0820043i
$914$		0			0
$915$	6.80949	−	9.21334i	0.225115	−	0.304584i
$916$		0			0
$917$	75.9250			2.50726
$918$		0			0
$919$	23.7372			0.783019			0.391509	−	0.920174i	$-0.371953\pi$
$919$	23.7372			0.783019			0.391509	+	0.920174i	$0.371953\pi$
$920$		0			0
$921$	−12.2052	−	28.0268i	−0.402174	−	0.923515i
$922$		0			0
$923$	−28.0647	−	10.2147i	−0.923761	−	0.336222i
$924$		0			0
$925$	2.43538	−	13.8117i	0.0800747	−	0.454126i
$926$		0			0
$927$	−22.1322	−	14.3374i	−0.726916	−	0.470902i
$928$		0			0
$929$	1.36575	−	0.497092i	0.0448088	−	0.0163091i	−0.319519	−	0.947580i	$-0.603521\pi$
$929$	1.36575	−	0.497092i	0.0448088	−	0.0163091i	0.364327	+	0.931271i	$0.381299\pi$
$930$		0			0
$931$	−1.32833	+	1.11461i	−0.0435344	+	0.0365297i
$932$		0			0
$933$	13.4885	−	8.93874i	0.441592	−	0.292641i
$934$		0			0
$935$	−1.02716	−	1.77909i	−0.0335917	−	0.0581826i
$936$		0			0
$937$	5.05751	−	8.75987i	0.165222	−	0.286172i	−0.771512	−	0.636214i	$-0.780499\pi$
$937$	5.05751	−	8.75987i	0.165222	−	0.286172i	0.936734	+	0.350042i	$0.113833\pi$
$938$		0			0
$939$	9.05304	−	2.17883i	0.295435	−	0.0711036i
$940$		0			0
$941$	9.55560	+	54.1925i	0.311504	+	1.76662i	0.591189	+	0.806533i	$0.298659\pi$
$941$	9.55560	+	54.1925i	0.311504	+	1.76662i	−0.279686	+	0.960092i	$0.590230\pi$
$942$		0			0
$943$	−0.660119	−	0.553905i	−0.0214964	−	0.0180376i
$944$		0			0
$945$	−9.77172	+	8.37442i	−0.317874	+	0.272420i
$946$		0			0
$947$	19.9934	+	16.7765i	0.649699	+	0.545162i	0.906980	−	0.421175i	$-0.138382\pi$
$947$	19.9934	+	16.7765i	0.649699	+	0.545162i	−0.257281	+	0.966337i	$0.582826\pi$
$948$		0			0
$949$	1.11282	+	6.31110i	0.0361236	+	0.204867i
$950$		0			0
$951$	−6.68516	+	22.6155i	−0.216781	+	0.733357i
$952$		0			0
$953$	25.2220	−	43.6858i	0.817022	−	1.41512i	−0.0908457	−	0.995865i	$-0.528957\pi$
$953$	25.2220	−	43.6858i	0.817022	−	1.41512i	0.907867	−	0.419258i	$-0.137710\pi$
$954$		0			0
$955$	−4.62735	−	8.01480i	−0.149737	−	0.259353i
$956$		0			0
$957$	13.0609	+	6.50277i	0.422200	+	0.210205i
$958$		0			0
$959$	−76.5760	+	64.2549i	−2.47277	+	2.07490i
$960$		0			0
$961$	−23.5692	+	8.57850i	−0.760298	+	0.276726i
$962$		0			0
$963$	38.3999	+	8.81980i	1.23742	+	0.284214i
$964$		0			0
$965$	1.68354	−	9.54782i	0.0541950	−	0.307355i
$966$		0			0
$967$	−6.30107	−	2.29340i	−0.202629	−	0.0737509i	0.238712	−	0.971090i	$-0.423275\pi$
$967$	−6.30107	−	2.29340i	−0.202629	−	0.0737509i	−0.441341	+	0.897340i	$0.645497\pi$
$968$		0			0
$969$	0.531373	+	0.0602393i	0.0170702	+	0.00193516i
$970$		0			0
$971$	−47.8500			−1.53558			−0.767789	−	0.640703i	$-0.778643\pi$
$971$	−47.8500			−1.53558			−0.767789	+	0.640703i	$0.778643\pi$
$972$		0			0
$973$	−89.8206			−2.87952
$974$		0			0
$975$	17.3872	+	1.97111i	0.556836	+	0.0631259i
$976$		0			0
$977$	−10.9385	−	3.98129i	−0.349954	−	0.127373i	0.161061	−	0.986944i	$-0.448508\pi$
$977$	−10.9385	−	3.98129i	−0.349954	−	0.127373i	−0.511015	+	0.859572i	$0.670730\pi$
$978$		0			0
$979$	0.229823	−	1.30339i	0.00734517	−	0.0416565i
$980$		0			0
$981$	−40.7601	−	9.36188i	−1.30137	−	0.298902i
$982$		0			0
$983$	40.4922	−	14.7380i	1.29150	−	0.470068i	0.397282	−	0.917696i	$-0.369953\pi$
$983$	40.4922	−	14.7380i	1.29150	−	0.470068i	0.894220	+	0.447628i	$0.147731\pi$
$984$		0			0
$985$	8.75358	−	7.34512i	0.278912	−	0.234035i
$986$		0			0
$987$	−15.4371	−	7.68583i	−0.491370	−	0.244643i
$988$		0			0
$989$	0.0238188	+	0.0412554i	0.000757394	+	0.00131185i
$990$		0			0
$991$	−21.4178	+	37.0967i	−0.680359	+	1.17842i	0.294512	+	0.955648i	$0.404843\pi$
$991$	−21.4178	+	37.0967i	−0.680359	+	1.17842i	−0.974871	+	0.222769i	$0.928491\pi$
$992$		0			0
$993$	−2.85571	+	9.66070i	−0.0906234	+	0.306573i
$994$		0			0
$995$	−1.44579	−	8.19947i	−0.0458345	−	0.259941i
$996$		0			0
$997$	18.0764	+	15.1679i	0.572484	+	0.480371i	0.882469	−	0.470370i	$-0.155880\pi$
$997$	18.0764	+	15.1679i	0.572484	+	0.480371i	−0.309985	+	0.950741i	$0.600324\pi$
$998$		0			0
$999$	2.85337	+	15.2516i	0.0902766	+	0.482539i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.y.a.97.8	yes	48
4.3	odd	2	inner	864.2.y.a.97.1	✓	48
27.22	even	9	inner	864.2.y.a.481.8	yes	48
108.103	odd	18	inner	864.2.y.a.481.1	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.y.a.97.1	✓	48	4.3	odd	2	inner
864.2.y.a.97.8	yes	48	1.1	even	1	trivial
864.2.y.a.481.1	yes	48	108.103	odd	18	inner
864.2.y.a.481.8	yes	48	27.22	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.y (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.72103 + 0.195105i) q^{3} +(0.517524 + 0.188363i) q^{5} +(-0.780902 + 4.42872i) q^{7} +(2.92387 + 0.671562i) q^{9} +O(q^{10})\)	\(q+(1.72103 + 0.195105i) q^{3} +(0.517524 + 0.188363i) q^{5} +(-0.780902 + 4.42872i) q^{7} +(2.92387 + 0.671562i) q^{9} +(-1.48871 + 0.541847i) q^{11} +(-1.64780 + 1.38267i) q^{13} +(0.853922 + 0.425150i) q^{15} +(1.17725 + 2.03906i) q^{17} +(0.0655666 - 0.113565i) q^{19} +(-2.20802 + 7.46958i) q^{21} +(-0.0132392 - 0.0750834i) q^{23} +(-3.59787 - 3.01897i) q^{25} +(4.90103 + 1.72624i) q^{27} +(-4.07315 - 3.41778i) q^{29} +(1.30041 + 7.37501i) q^{31} +(-2.66783 + 0.642078i) q^{33} +(-1.23834 + 2.14487i) q^{35} +(1.49305 + 2.58604i) q^{37} +(-3.10567 + 2.05811i) q^{39} +(8.65824 - 7.26512i) q^{41} +(-0.587142 + 0.213702i) q^{43} +(1.38667 + 0.898299i) q^{45} +(-0.384448 + 2.18031i) q^{47} +(-12.4259 - 4.52265i) q^{49} +(1.62825 + 3.73896i) q^{51} +9.94034 q^{53} -0.872508 q^{55} +(0.134999 - 0.182656i) q^{57} +(5.48455 + 1.99621i) q^{59} +(2.08556 - 11.8278i) q^{61} +(-5.25741 + 12.4246i) q^{63} +(-1.11322 + 0.405179i) q^{65} +(10.0979 - 8.47314i) q^{67} +(-0.00813594 - 0.131804i) q^{69} +(6.94216 + 12.0242i) q^{71} +(1.48961 - 2.58009i) q^{73} +(-5.60302 - 5.89770i) q^{75} +(-1.23715 - 7.01621i) q^{77} +(1.90882 + 1.60169i) q^{79} +(8.09801 + 3.92712i) q^{81} +(-3.50308 - 2.93943i) q^{83} +(0.225172 + 1.27701i) q^{85} +(-6.34317 - 6.67678i) q^{87} +(-0.417704 + 0.723484i) q^{89} +(-4.83667 - 8.37736i) q^{91} +(0.799146 + 12.9463i) q^{93} +(0.0553237 - 0.0464221i) q^{95} +(-12.6541 + 4.60571i) q^{97} +(-4.71668 + 0.584527i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 12 q^{9}+O(q^{10}) \) 48 * q - 12 * q^9	\( 48 q - 12 q^{9} - 12 q^{17} - 48 q^{21} + 24 q^{25} + 6 q^{29} - 6 q^{33} + 30 q^{37} - 12 q^{41} + 30 q^{45} - 6 q^{49} - 36 q^{53} - 6 q^{57} - 12 q^{61} - 60 q^{65} - 78 q^{69} + 48 q^{73} - 12 q^{77} - 36 q^{81} + 102 q^{85} - 66 q^{89} + 36 q^{93} + 6 q^{97}+O(q^{100}) \) 48 * q - 12 * q^9 - 12 * q^17 - 48 * q^21 + 24 * q^25 + 6 * q^29 - 6 * q^33 + 30 * q^37 - 12 * q^41 + 30 * q^45 - 6 * q^49 - 36 * q^53 - 6 * q^57 - 12 * q^61 - 60 * q^65 - 78 * q^69 + 48 * q^73 - 12 * q^77 - 36 * q^81 + 102 * q^85 - 66 * q^89 + 36 * q^93 + 6 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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